TY - JOUR

T1 - A model of Internet topology using k-shell decomposition

AU - Carmi, Shai

AU - Havlin, Shlomo

AU - Kirkpatrick, Scott

AU - Shavitt, Yuval

AU - Shir, Eran

PY - 2007/7/3

Y1 - 2007/7/3

N2 - We study a map of the Internet (at the autonomous systems level), by introducing and using the method of k-shell decomposition and the methods of percolation theory and fractal geometry, to find a model for the structure of the Internet. In particular, our analysis uses information on the connectivity of the network shells to separate, in a unique (no parameters) way, the Internet into three subcomponents: (i) a nucleus that is a small (≈100 nodes), very well connected globally distributed subgraph; (ii) a fractal subcomponent that is able to connect the bulk of the Internet without congesting the nucleus, with self-similar properties and critical exponents predicted from percolation theory; and (iii) dendrite-like structures, usually isolated nodes that are connected to the rest of the network through the nucleus only. We show that our method of decomposition is robust and provides insight into the underlying structure of the Internet and its functional consequences. Our approach of decomposing the network is general and also useful when studying other complex networks.

AB - We study a map of the Internet (at the autonomous systems level), by introducing and using the method of k-shell decomposition and the methods of percolation theory and fractal geometry, to find a model for the structure of the Internet. In particular, our analysis uses information on the connectivity of the network shells to separate, in a unique (no parameters) way, the Internet into three subcomponents: (i) a nucleus that is a small (≈100 nodes), very well connected globally distributed subgraph; (ii) a fractal subcomponent that is able to connect the bulk of the Internet without congesting the nucleus, with self-similar properties and critical exponents predicted from percolation theory; and (iii) dendrite-like structures, usually isolated nodes that are connected to the rest of the network through the nucleus only. We show that our method of decomposition is robust and provides insight into the underlying structure of the Internet and its functional consequences. Our approach of decomposing the network is general and also useful when studying other complex networks.

KW - Fractals

KW - Networks

KW - Percolation

UR - http://www.scopus.com/inward/record.url?scp=34547413871&partnerID=8YFLogxK

U2 - 10.1073/pnas.0701175104

DO - 10.1073/pnas.0701175104

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C2 - 17586683

AN - SCOPUS:34547413871

SN - 0027-8424

VL - 104

SP - 11150

EP - 11154

JO - Proceedings of the National Academy of Sciences of the United States of America

JF - Proceedings of the National Academy of Sciences of the United States of America

IS - 27

ER -